Question

0.1311(22 2z1 5. The transfer function of a system is H(z) = z2-0.74780.2722 a) Find the frequency response function of the system b) Let xn] 1 cos(0.2nt)+cos(0.45n7). Find the steady-state response. Use Matlab c) Plot the magnitude and phase response using Matlab

Answer 1

HC2) 22 o472o,272a e o4e

MATLAB:

clc;close all;clear all;

b=[0.1311 2*0.1311 0.1311]
a=[1 -0.7478 0.2722]

figure;
n=0:1:50
x=1+(cos(0.2*n*pi))+(cos(0.45*n*pi))
y=filter(b,a,x)
subplot(211)
stem(n,x,'r')
xlabel('n')
ylabel('x(n)')
title('x(n)')
subplot(212)
stem(n,y,'m')
xlabel('n')
ylabel('y(n)')
title('y(n)')

figure;
freqz(b,a)

Plots:

x(n) n y(n) 0. 30 10 50 50 40 40 30 20 20 LO (u)x (u)A

0 20 -40 -60 -80 -100 -120 0 0.8 0.6 0.4 0.2 Normalized Frequency (xt rad/sample) -100 P-150 -200 0.8 0.6 0.4 0.2 Normalized Frequency (xit rad/sample) Magnitude (dB) Phase (degrees) 50